Agreed, 0.4fb/d is a relief after all of those small dumped fills.
They’re roughly 10fb behind 2016 - by looking at the lumiplots, no science here - so as you said unless they unlock some luminosity somewhere, the 40fb are probably out of reach. Maybe beta 30cm would give a boost (assumimg they can get the optics and machine protection stuff done quickly)

Interesting... so am I right in saying that the beam can heat the pipe via inductive heating, thus releasing any frozen gas, and temporary failing of the cryogenics then adds to the problem as the frozen gas is heated?

This makes sense because the problem seemed to go away for a while as they gradually reached 1.7\nb/s, with the pumps able to handle the gradual increase of gas. The problem then suddenly reappearing when they stepped up the intensity further going for close to 2.0\nb/s; which released excessive gas.

If so, then there shouldn't be too much of a problem doing what they did before: slowly increasing the intensity once again, reducing the intensity as gas is released and removed by the pumps, then slowly increasing again etc. The good news is that despite the gas release, the LHC can still run at its design specification still reaching x2 this if the increase is done carefully and slowly.

2 fill attempts with 2556 bunches, both dumped during ramp due to 16L2.
7 fill attempts with 2220 bunches, 5 dumped during ramp due to 16L2, one dumped before SB for another reason, only one reached SB - only to get dumped by 16L2 later.
3 fill attempts with 1932 bunches, one dumped during ramp, one before SB, one in SB, all due to 16L2.
16 fill attempts with 1740 bunches, 5 dumped during ramp due to 16L2, 11 reached SB, and only 2 of these got dumped due to 16L2 later.
Some attempts with lower numbers of bunches, also with a high 16L2 dump rate.

1550 bunches had some reasonable success recently. 1700 with gaps in the bunch trains is discussed, going to 50 ns bunch spacing (with a maximum of 1500 bunches) is discussed as well.

So running with the current 1550b yields 0.3\fb/day = 2\fb/week at 55% efficiency giving 35 - 40\fb for 2017 which looks fine to me, bearing in mind that the hope was to accumulate > 100\fb for run 2. I don't see the point in changing the planned running parameters of the LHC significantly, just for the sake of an extra ~10\fb.

"On the basis of current statistics, there appears to be no direct correlation between the number of bunches and the number of beam dumps, so the task force is now planning tests with beams of up to 2200 bunches (last year’s maximum) to evaluate the situation."

It looks as if they've reallocated two weeks from the proton-proton run to 5 TeV p-p Reference
& Low Energy High Beta run. Currently hitting > 3\fb/week so ~ 45\fb for the remaining 7 weeks still looks realistic.